Variations on the Convolutional Sparse Coding Model

Over the past decade, the celebrated sparse representation model has achieved impressive results in various signal and image processing tasks. A convolutional version of this model, termed convolutional sparse coding (CSC), has been recently reintroduced and extensively studied. CSC brings a natural...

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Veröffentlicht in:IEEE transactions on signal processing Jg. 68; S. 519 - 528
Hauptverfasser: Rey-Otero, Ives, Sulam, Jeremias, Elad, Michael
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York IEEE 2020
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
Algorithms
Coding
convex optimization
Convolution
Convolutional codes
convolutional sparse coding
Dictionaries
Formulations
Image coding
Image processing
Image reconstruction
Norms
parallel proximal algorithm
Representations
Signal processing
Signal processing algorithms
Silicon
Sparse representation
ISSN:1053-587X, 1941-0476
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Zusammenfassung:Over the past decade, the celebrated sparse representation model has achieved impressive results in various signal and image processing tasks. A convolutional version of this model, termed convolutional sparse coding (CSC), has been recently reintroduced and extensively studied. CSC brings a natural remedy to the limitation of typical sparse enforcing approaches of handling global and high-dimensional signals by local, patch-based, processing. While the classic field of sparse representations has been able to cater for the diverse challenges of different signal processing tasks by considering a wide range of problem formulations, almost all available algorithms that deploy the CSC model consider the same \ell _1 - \ell _2 problem form. As we argue in this paper, this CSC pursuit formulation is also too restrictive as it fails to explicitly exploit some local characteristics of the signal. This work expands the range of formulations for the CSC model by proposing two convex alternatives that merge global norms with local penalties and constraints. The main contribution of this work is the derivation of efficient and provably converging algorithms to solve these new sparse coding formulations.
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ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2020.2964239